Bodie Island is awesome because it still uses a fresnel lens that flashes versus a constant rotating light like the Cape Hatteras Lighthouse. I just looked up the interval times and according to wikipeida the bulb stays on 2.5 seconds, 2.5 seconds off, 2.5 seconds on, and 22.5 seconds eclipse with 2 cycles each minute. The key thing to use here is a remote to control the shutter. I always tried to aim for the last 1/2 second where the light is leaving the bulb on the second flash. If you do that it leaves roughly ~20 seconds before the cycle starts over so the bulb doesn't get blown out.
Good luck and I always found if I went between 10pm and sunrise I'd usually have the site to myself.